Mathematical Statistics

Course Overview

This is an introductory course in Mathematical Statistics. The objective is to know the fundamental tools of probability that are needed to understand statistics. Some topics that need to be mastered are Joint Distributions, Limit Theorems, Estimation, Confidence Intervals, and Analysis of Variance. The course will possess mainly three components:

• Review and Understanding of Probability: A brief review of the basic concepts in probability and the introduction to new ones will be given. An important emphasis will be put on conditional probability and independence as they are the foundation of modern probability and statistics.
• Estimation, Testing and Confidence Regions: An exploration on the usage of probability techniques used in statistics will be given. A critical idea will be to find parameters or regions for high probability, where successive repetition of the experiment will yield an important estimate of where such parameter lies. This parameter can then be used to explain a model from which the data comes from allowing us to then test hypotheses.
• Learn the usage of R in Statistics: Basic techniques on how to explore, interpret and analyze data to perform statistic tests will be investigated. It will become critical to learn how to use R as a tool to help in the visualization and understanding of the most important concepts in mathematical Statistics.

Prerequisites

• MTH 451.

Textbooks

• Probability and Mathematical Statistics: Theory, Applications, and Practice in R by Mary C. Meyer. SIAM.

Grading

• Midterm Exam 1: 20%
• Midterm Exam 2: 20%
• Homework: 20%
• Participation: 10%
• Cumulative Final Exam: 30%